I'd say temps in the high 40s to low 50s with near silent operation.
My aircooled 470 has a 70mm fan from an AMD heatsink and one of the stock 80mm fans from the twin frozr cooler because the other stock fan broke, it's getting the air from my watercooled card's rad and they're both overclocked.

Both cards and my CPU have been folding 24/7 for about five days at somewhere near a 21C ambient temperature and it's topped out at 63C at 60% fan with the AMD fan at full speed.

My card needs over 200W to function so that cooler should cool yours with absolutely no problems.

Edit: At stock speed when I had two fans blowing fresh air straight at my card and not through the radiator at my card I was getting a max temp of 53-54 so that's why I say high 40s is what I'd expect you to get. If you've got good airflow in your case that is.Edited by Mike-IRL - 6/22/11 at 9:14am

Edit 2:
if OP has a non reference 5770 (eg Asus CuCore as shown in pic 4 below) that has no connector on the entire length of the 2nd slot (green arrow), then the Accelero Twin Turbo Pro might fit.

Twin Turbo Pro has a clearance of 14.3mm (pic 2) while the thickness of the PCB plus DVI port is about 12.2mm (pic 5). So, there is a 2mm clearance. Member mauley has reported that the Twin Turbo Pro can fit into his non reference Asus 5770 CuCore. Note post #2 of the link below also contains temperature numbers.

Twin Turbo Pro is the way to go! I keep my fan speed at 100% at all times and it's silent and cools incredibly. The RAM sinks are horrid though. My Sapphire 5850 loads at 48c max but the RAM goes up to 90c. The RAM never got that hot with the stock cooler.